טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentSpivakovsky Alexander
SubjectAlgorithms for Solving Large-Scale Regularized Structured
Total Least Squares Problems
DepartmentDepartment of Industrial Engineering and Management
Supervisor Professor Amir Beck
Full Thesis textFull thesis text - English Version


Abstract

In this work, we seek an estimate to the solution of the linear system Ab ? b, where b is submitted to noise, and A is submitted to structured noise. To stabilize the solution, we add a convex regularization function R(x). The arising problem is the so-called regularized structured total least squares (RSTLS) problem.

We develop several algorithms for a smooth and quadratic regularization

R(x) = ||Gx||2. In particular, we propose a block-coordinate descent method, and an accelerated gradient algorithm. The methods have been specially adapted to deal with image deblurring problems, exploiting fast Fourier/cosine transforms. We also propose gradient-based methods for the RSTLS problem with nonsmooth regularizer such as total variation and the l1 norm of a wavelet transform. Several numerical experiments demonstrate the effectiveness of the suggested algorithms.